Question

if alpha and beta are the roots of x2 - 2x- 1 =0 then find the value of alpha square beta +beta square alpha

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer: -2

Step-by-step explanation:

Given : $x^{2} - 2x - 1 = 0$

α and β are the roots of the equation.

To find : $\alpha ^{2} \beta + \beta ^{2} \alpha$

Solution :

∴ Sum of roots = α + β = -(-2) = 2

∴ Product of roots = αβ = -1/1 = -1

⇒ $\alpha ^{2} \beta + \beta ^{2} \alpha$

⇒ αβ(α + β)

⇒ -1(2)

= -2

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